One of the new displays inside the redeveloped National Army Museum.
Photograph: Nicky J Sims/PR

The Duke of Wellington’s cloak, the skeleton of Napoleon’s horse, Lawrence of Arabia’s robes, the cloak worn by the man who carried the order to the front for the Charge of the Light Brigade, and a twisted piece of shrapnel from an encounter 11 years ago in Helmand province in Afghanistan: these are among the new displays at the National Army Museum in London, which reopens this week after a three-year, £23.75m redevelopment.

The shrapnel still contains part of the uniform sleeve of Sgt Maj Andrew Stockton, and almost certainly part of his arm.

“To me this is an amazing object, equally if not more amazing than some of the most famous things in our collection for the story it can tell,” said the museum curator Sophie Stathi.

Nearby is displayed the surgical saw used to remove part of the Earl of Uxbridge’s right leg after one of the most famously laconic exchanges in military history. After being struck by a cannonball on the Waterloo battlefield, Uxbridge remarked, “By God, sir, I’ve lost my leg,” to which the Duke of Wellington responded “By God, sir, so you have.” After the amputation, Uxbridge remarked only that the saw had been somewhat blunt: the leg itself was given a small tomb near the battlefield and displayed to tourists by a local entrepreneur.

Stockton, of the 32 Regiment Royal Artillery, displayed almost equal sang froid when in 2006 he was on a routine patrol in Helmand that ran into a Taliban ambush: he was hit by a rocket-launched grenade that shattered his left arm. Stockton pinched his own torn arteries together until medical help arrived and a tourniquet was applied: his arm was later amputated above the elbow.

Janice Murray, the director of the museum, said: “I don’t think that you can understand British history if you don’t understand the history of the British army – the British army in many ways has shaped the country we are living in today.”

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Among stories of famous deeds and heroic battles the museum includes accounts of centuries of moaning about conditions, leadership, uniform – and rations. “Very frequently in the summer season when we had been some time on the march, our meat was literally like carrion,” the soldier John Green recalled of the Peninsular campaign in 1808.

The curator Chris Cooper said the complaints were largely justified, with even the most modern ration packs supplying too few calories. “It is remarkable how little has changed, from the civil war to the present day, in how deficient ration packs are in terms of the task soldiers are asked to do.”

The museum, first housed in former stables at the military academy at Sandhurst, opened in 1971 next door to the Chelsea pensioners in London. Despite repeated efforts to extend and improve it, the building had dark confusing interiors and a bewildering assortment of floor levels. The rebuild by BDP architects, which was partly paid for by a Heritage Lottery Fund grant of £11.5m, has given it a front door directly on to the road and new galleries around an airy atrium. The museum hopes the changes will increase visitor numbers from the 247,000 before it closed to 400,000.

National Army Museum, Royal Hospital Road, London, open daily from 30 March, admission free